dgnd {cmgnd}R Documentation

The Generalized Normal Distribution (GND)

Description

Density function for the GND with location parameter mu, scale parameter sigma and shape parameter nu.

Usage

dgnd(x, mu = 0, sigma = 1, nu = 2)

Arguments

x

A numeric vector of observations.

mu

A numeric value indicating the location parameter \mu.

sigma

A numeric value indicating the scale parameter \sigma.

nu

A numeric value indicating the shape parameter \nu.

Details

If mu, sigma and nu are not specified they assume the default values of 0, 1 and 2, respectively. The GND distribution has density

f_{GND}(x|\mu,\sigma,\nu)=\frac{\nu}{2\sigma\Gamma(1\mathbin{/}\nu)}\exp\Biggr\{-\Biggr|\frac{x-\mu}{\sigma}\Biggr|^\nu\Biggr\}.

The shape parameter \nu controls both the peakedness and tail weights. If \nu=1 the GND reduces to the Laplace distribution and if \nu=2 it coincides with the normal distribution. It is noticed that 1<\nu<2 yields an intermediate distribution between the normal and the Laplace distribution. As limit cases, for \nu\rightarrow\infty the distribution tends to a uniform distribution, while for \nu\rightarrow0 it will be impulsive.

Value

dgnd returns the density.

References

Nadarajah, S. (2005). A generalized normal distribution. Journal of Applied Statistics, 32(7):685–694.


[Package cmgnd version 0.1.1 Index]